Abstract. We show that both the triaxial rotor model and the anharmonic vibrator model with phonon mixing exhibit a global correlation between the quadrupole moments of the two lowest 2+ states in collective nuclei, which had previously been observed in experimental data across the periodic table. We then derive other electromagnetic properties for these two models of nuclear structure and compare them with experimental data. We find that both robustly describe the data over the region of nuclei for which the models are applicable, including many that they have in common. We then show that there seems to exist a robust orthogonal transformation between these two models for realistic nuclear systems, suggesting that these two seemingly diverse descriptions of quadrupole collective phenomena seem to act in a similar model space and may therefore have a common origin.